This invention relates to a method and apparatus for measuring the thicknesses of film layers of different kinds of synthetic resins forming a composite multilayer film or sheet by utilizing infrared rays.
For measuring the film thickness of a single-layer plastic film made of a polymer of polyethylene, polypropylene, polyvinyl chloride, polyvinylidene chloride or the like, there have heretofore been employed thickness gauges using .beta. rays and infrared rays, and these gauges have been widely used in many industrial fields. However, there have not been proposed effective methods and apparatus for measuring the thicknesses of individually laminated polymer film layers of a composite multilayer film. In the prior art, the cross section of a composite multilayer plastic film (hereinafter referred to as a multilayer film) is enlarged by a microscope or projector to measure the thickness of each film layer of the film by the human eyes. This method is time-consuming and troublesome and subject to measurement errors due to each measuring person's individual difference and incapable of on-line and noncontact measurement, so that the measured values cannot be used as effective process control information. The conventional method presents a problem also in merely measuring the total thickness of the multilayer film. The total thickness value of the multilayer film measured by the .beta.-ray thickness gauge, usually employed for measuring the single-layer film thickness, do not in some cases agree with the total thickness value measured by a dial gauge, depending upon a combination of polymers of the layers of the multilayer film. The reason is as follows: The .beta.-ray thickness gauge is to measure the film thickness based on the degree of scattering of .beta. rays depending upon the density of the film to be measured. In the case of a multilayer film composed of film layers of different densities, such as a polyethylene (0.9 in density) layer and a polyvinylidene chloride (1.5 in density), even if the total film thickness does not change, the thicknesses of the two film layers vary relative to each other. Since the amount of scattering of .beta. rays is determined by the weights that the thicknesses of the respective film layers are multiplied by their densities, the total amount of scattering of .beta. rays varies with a change in the thickness ratio of the film layers to provide an erroneous measured value as if the total thickness has changed.
Further, for measuring the multilayer film, it is possible to provide an infrared thickness gauge for a single-layer film for each of the layers of different components or to provide such infrared thickness gauges as one assembly. With this method, however, it is very difficult in practice to measure the thickness of each film layer without being affected by the other film layers. For example, for measuring a multilayer film composed of two layers A and B of different polymers, in the apparatus using conventional infrared single-layer film thickness gauges in combination, three different wavelengths of infrared rays used are selected as follows:
(1) Wavelength .lambda..sub.R
A reference wavelength of an infrared ray which is hardly absorbed by either of the film layers A and B.
(2) Wavelength .lambda..sub.1
A sample wavelength for the film layer A, which is the wavelength of an infrared ray which is strongly absorbed by the film layer A but hardly absorbed by the film layer B.
(3) Wavelength .lambda..sub.2
A sample wavelength for the film layer B, which is the wavelength of an infrared ray which is strongly absorbed by the film layer B but hardly absorbed by the film layer A.
The above three wavelengths are selected and, from the amounts of transmitted infrared lights at the respective wavelengths, the thicknesses of the film layers are measured. Their relationships, expressed for the sake of simplicity, are as follows: EQU I(.lambda..sub.1)=I.sub.0 (.lambda..sub.1)e.sup.-.alpha.(.lambda..sbsp.1.sup.)d.sbsp.A EQU I(.lambda..sub.2)=I.sub.0 (.lambda..sub.2)e.sup.-.alpha.(.lambda..sbsp.2.sup.)d.sbsp.B ( 1) EQU I(.lambda..sub.R)=I.sub.0 (.lambda..sub.R)e.sup.-.alpha.(.lambda..sbsp.R.sup.)(d.sbsp.A.sup.+d.sbsp. B.sup.)
where I.sub.0 (.lambda..sub.1), I.sub.0 (.lambda..sub.2) and I.sub.0 (.lambda..sub.R) are the intensities of infrared lights of the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R before they enter the film layers A and B to be measured; I(.lambda..sub.1), I(.lambda..sub.2) and I(.lambda..sub.R) are the intensities of infrared lights of the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R after absorbed by the film layers A and B; .alpha.(.lambda..sub.1), .alpha.(.lambda..sub.2) and .alpha.(.lambda..sub.R) are the infrared absorption coefficients of the film layers A and B at the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R ; and d.sub.A and d.sub.B are the thicknesses of the film layers A and B. The infrared ray of the wavelength .lambda..sub.R is scarcely absorbed by the film layers A and B, that is, .alpha.(.lambda..sub.R)=0, and in the case where the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R are close to one another, the infrared radiation may be approximate to I.sub.0 (.lambda..sub.1)=I.sub.0 (.lambda..sub.2)=I.sub.0 (.lambda..sub.R) Accordingly, if I(.lambda..sub.1) and I(.lambda..sub.2) are respectively divided by I(.lambda..sub.R) in the equation (1), it follows that ##EQU1##
In other words, the ratio between the amounts of film transmitted lights at the wavelengths .lambda..sub.1 and .lambda..sub.R corresponds to the thickness d.sub.A through the absorption coefficient .alpha.(.lambda..sub.1), the ratio between the amounts of film transmitted lights at the wavelengths .lambda..sub.2 and .lambda..sub.R corresponds to the thickness d.sub.B through the absorption coefficient .alpha.(.lambda..sub.2).
Therefore, by measuring changes in the two ratios, the thicknesses of the film layers A and B are measured. This is the basic idea of the conventional multilayer film thickness gauge using single-layer film thickness gauges in combination. However, it is very difficult in practice to select the wavelengths .lambda..sub.1 and .lambda..sub.2 of infrared lights each of which is strongly absorbed by one of the film layers of the multilayer film but hardly absorbed by the other film layer; and even if they can be selected, measurement is limited to multilayer films having film layers of severely restricted combinations of polymers. Further, even if a suitable combination of polymers is obtained, all the wavelengths used may, in a certain case, not lie within the detection wavelength range of one detector, resulting in the necessity of providing detectors of different other kinds. But, owing to the problem of linearity of the sensitivity of each of the detector to the amount of light relative to the other detectors, a change in the sensitivity of each detector with temperature, etc. it is very difficult to obtain an apparatus in practical use. Moreover, the infrared ray of the absorption wavelength peculiar to one film layer is also absorbed by the other film layer, and variations of the thickness of the other film layer exerts an influence upon the amounts of transmitted infrared light of the absorption wavelength for the layer being measured; therefore, the influence between the film layers cannot be removed.
An object of this invention is to provide an infrared multilayer film thickness measuring method and apparatus by which the thicknesses of layers of synthetic resins forming a multilayer film or sheet can be accurately measured in a noncontact manner.
Another object of this invention is to provide an infrared multilayer film thickness measuring method and apparatus by which even if an infrared ray of a sample wavelength for one film layer is also absorbed by other film layers, the thicknesses of the individual film layers can be measured, so that the thickness of each film layer can be accurately measured irrespective of variations of the thicknesses of the other film layers.
Still another object of this invention is to provide an infrared multilayer film thickness measuring method and apparatus with which it is possible to rapidly and accurately measure the thickness of each of film layers of a multilayer film through it.
In accordance with this invention, infrared rays of at least a plurality of sample wavelengths and one or more reference wavelength are projected to a multilayer film or sheet composed of a plurality of film layers made of different synthetic resins. The sample wavelengths each correspond to one of the plurality of different film layers of the multilayer film or sheet and is one of infrared absorption wavelengths of the film layer. Each sample wavelength corresponding to one of the film layers may also coincide with any of the infrared absorption wavelengths of the other film layers; therefore, the infrared absorption wavelengths of each film layer coincide with at least one of the sample wavelengths. The reference wavelength is selected to differ from any of the infrared absorption wavelengths of the respective film layers.
The amounts of infrared lights of each sample wavelength and the reference wavelength which have passed through the multilayer film at least once is normalized by obtaining the ratio between them. The infrared rays of the sample wavelengths and the reference wavelength are projected onto the multilayer film from a projector unit while being switched in a sequential order. The transmitted lights are converted by a photo detector unit to electric signals to derive therefrom respective wavelength components in synchronism with the switching in the projector unit. Alternatively, the infrared rays of only the sample wavelengths and the reference wavelength or infrared rays including those of such wavelengths are simultaneously projected onto the multilayer film and the respective wavelength components are optically separated from the transmitted light and then they are converted by individual photo detector units to electrical signals. The ratios between sample signals which are the thus obtained electric signals representing the intensities of lights of the sample wavelength and a reference signal indicating the intensity of light of the reference wavelength, are respectively taken.
To obtain the transmitted light, the projector unit and the photo detector unit are disposed across the multilayer film to be measured and an infrared ray having passed through the multilayer film once is received by the photo detector unit. In the case where the multilayer film has been deposited on its one side with an infrared ray reflecting layer, such as, for example, an aluminum foil layer, the projector unit and the photo detector unit are both disposed on the side opposite from the reflecting layer of the multilayer film. In this case, the projected infrared ray enters the multilayer film and it is reflected and scattered by the reflecting layer and is then received by the photo detector unit; namely, the infrared ray having twice passed through the multilayer film is received by the photo detector unit. It is also possible to place the projector unit and the photo detector unit on one side of the multilayer film to be measured and a reflector unit on the other side. In such a case, the infrared ray from the projector unit, having passed through the multilayer film, is reflected from the reflector unit back to the direction of incidence to pass through the multilayer film again along the same light path that the incident light followed, and one portion of this reflected light is branched to the photo detector unit. The aforesaid ratios are derived from such a transmitted light transmitted through the multilayer film at least once and received by the photo detector unit.
The thicknesses of the individual film layers are obtained by an operation for solving a simultaneous equation in which the abovesaid ratios, the absorption coefficients of the film layers at the sample and reference wavelengths are used as coefficient and the thicknesses of the film layers are used as unknowns.
For the sake of simplicity, a description will be given in connection with the case where the multilayer film to be measured consists of two film layers A and B made of polymers of different kinds. The film layers A and B both exhibit, in the infrared ray region, infrared absorption spectra having characteristic absorption peaks peculiar to the polymer films, respectively. Now, two arbitrary ones of the absorption peaks are selected and the wavelengths of the selected absorption peaks are represented by .lambda..sub.1 and .lambda..sub.2, respectively. In this case, it is possible to select as .lambda..sub.1 and .lambda..sub.2 the wavelengths of infrared lights which are absorbed by the both film layers A and B. The selected wavelength will hereinafter be referred to as the sample wavelengths .lambda..sub.1 and .lambda..sub.2, respectively. A wavelength of an infrared light which is different from the wavelengths of the abovesaid absorption peaks, that is, which is hardly absorbed by the film layers A and B, is selected as a reference wavelength .lambda..sub.R.
Generally, the following equation (3) is formed from an equation of transmission of light: EQU I(.lambda..sub.1)=I.sub.0 (.lambda..sub.1)e.sup.-(.alpha.(.lambda..sbsp.1.sup.)d.sbsp.A.sup.+.beta.( .lambda..sbsp.1.sup.)d.sbsp.B.sup.) EQU I(.lambda..sub.2)=I.sub.0 (.lambda..sub.2)e.sup.-(.alpha.(.lambda..sbsp.2.sup.)d.sbsp.A.sup.+.beta.( .lambda..sbsp.2.sup.)d.sbsp.B.sup.) ( 3) EQU I(.lambda..sub.R)=I.sub.0 (.lambda..sub.R)e.sup.-(.alpha.(.lambda..sbsp.R.sup.)d.sbsp.A.sup.+.beta.( .lambda..sbsp.R.sup.)d.sbsp.B.sup.)
where I.sub.0 (.lambda..sub.1), I.sub.0 (.lambda..sub.2) and I.sub.0 (.lambda..sub.R) are the intensities of infrared lights incident on the multilayer film at the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R, respectively; I(.lambda..sub.1), I(.lambda..sub.2) and I(.lambda..sub.R) are the intensities of transmitted infrared lights absorbed by the multilayer film at the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R, respectively; .alpha.(.lambda..sub.1), .alpha.(.lambda..sub.2) and .alpha.(.lambda..sub.R) are absorption coefficients peculiar to the film layer A at the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R, respectively; .beta.(.lambda..sub.1), .beta.(.lambda..sub.2) and .beta.(.lambda..sub.R) are absorption coefficients peculiar to the film layer B at the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R, respectively; and d.sub.A and d.sub.B are the thicknesses of the film layers A and B.
Normalizing the ratios between I(.lambda..sub.R) and I(.lambda..sub.1) and between I(.lambda..sub.R) and I(.lambda..sub.2), it follows that ##EQU2##
Further, taking natural logarithms of the both sides, it follows that ##EQU3##
As is evident from the equation (5), the ratios I.sub.O (.lambda..sub.1)/I.sub.O (.lambda..sub.R) and I.sub.O (.lambda..sub.2)/I.sub.O (.lambda..sub.R) are the ratios of the amounts of incident infrared lights at the respective wavelengths, and hence are constants which remain constant irrespective of variations in the amount of light of the light source.
Therefore, if the values of four absorption coefficients (.alpha.(.lambda..sub.1)-.alpha.(.lambda..sub.R)), (.beta.(.lambda..sub.1)-.beta.(.lambda..sub.R)), (.alpha.(.lambda..sub.2)-.alpha.(.lambda..sub.R)) and (.beta.(.lambda..sub.2)-.beta.(.lambda..sub.R)) are known in advance, it is possible to measure the thicknesses d.sub.A and d.sub.B of the film layers A and B of the multilayer film and its total thickness d.sub.A +d.sub.B by measuring the amounts of film transmitted lights at the wavelengths .lambda..sub.1, .lambda..sub.2 and .lambda..sub.R, taking the ratios I(.lambda..sub.1)/I(.lambda..sub.R) and I(.lambda..sub.2)/I(.lambda..sub.R) and solving a simultaneous quadratic equation in which the thicknesses d.sub.A and d.sub.B are unknowns. The arithmetic processing for the thicknesses is achieved based on the equation (5) and this requires previous setting up of parameters necessary for solving the equation (5). By measuring I(.lambda..sub.1), I(.lambda..sub.2) and I(.lambda..sub.R) in the state of no multilayer film being not provided, the values of -ln{I.sub.O (.lambda..sub.1)/I.sub.O (.lambda..sub.R)} and -ln{I.sub.O (.lambda..sub.2)/I.sub.O (.lambda..sub.R)} are determined. Since these values always remain constant even if a change occurs in the amount of light of the light source, they are set at the beginning of measurement and reset at proper times during measurement. Further, the absorption coefficients {.alpha.(.lambda..sub.1)-.alpha.(.lambda..sub.R)}, {.beta.(.lambda..sub.1)-.beta.(.lambda..sub.R)}, {.alpha.(.lambda..sub.2)-.alpha.(.lambda..sub.R)} and {.beta.(.lambda..sub.2)-.beta.(.lambda..sub.R)} must be obtained beforehand from the same multilayer film as that to be measured. Once these parameters have been set, by measuring the intensities of transmitted lights I(.lambda..sub.1), I(.lambda..sub.2) and I(.lambda..sub.R) from the multilayer film, the film thicknesses d.sub.A, d.sub.B and d.sub.A +d.sub.B can be obtained by the operation in accordance with the equation (5).
As described above, in the present invention, the simultaneous equation (5) is set up without ignoring the infrared absorption of the film layers A and B at the respective wavelengths corresponding thereto and the thicknesses of the film layers are operated based on the equation (5), so that high measurement accuracy can be obtained. Moreover, even if the sample wavelength, for example, .lambda..sub.1 coincides with the infrared absorption wavelength of the film layer B which does not correspond thereto, the thicknesses of the film layers can be measured.
For measuring the thickness of the entire area of running multilayer film, it is considered to perform the measurement while reciprocating the measuring apparatus in a direction perpendicular to the direction of travel of the multilayer film, that is, in its widthwise direction. In this case, if the projector unit and the photo detector unit are disposed on both sides of the multilayer film, the optical axis between the projector unit and the photo detector unit becomes out of alignment to cause an error in the measurement unless the positional and angular relationships of the projector unit and the photo detector unit to each other are held constant at all times. For such measurement, it is effective to provide the aforementioned reflector unit and dispose both of the projector unit and the photo detector unit on one side of multilayer film to be measured. As the reflector unit, it is preferred to employ a reflector which reflects the incident light back to the same direction as its direction of incidence, such as a corner cube, a corner cube array, a recurrent reflecting sheet or film. With the provision of such a reflector unit, the projector unit and the photo detector unit can be held as one body on the same side of the multilayer film; therefore, there is no fear of their optical axes getting out of alignment due to their movement and even if a little change occurs in the positional relationships of the projector unit and the photo detector unit to the reflector unit during movement, the incident light is always reflected by the action of the reflector unit back to the same light path, ensuring accurate measurement. In order that the light reflected from the reflector unit and again transmitted through the multilayer film may be branched to the photo detector unit, use may be made of, for example, a half mirror or a right-angled prism. By transmitting the incident light through the multilayer film twice, the absorption by the multilayer film is increased to provide for enhanced SN ratio. Consequently, the two-transmission system is suitable for measuring a film whose infrared absorption is small and is also effective for conducting measurement with the measuring apparatus fixed.